Multi-fuzzy sets: An extension of fuzzy sets

Sabu Sebastian () and T. V. Ramakrishnan
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Sabu Sebastian: Kannur University
T. V. Ramakrishnan: Kannur University

Fuzzy Information and Engineering, 2011, vol. 3, issue 1, 35-43

Abstract: Abstract In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic fuzzy set theory and L-fuzzy set theory.

Keywords: Multi-fuzzy set; Intuitionistic fuzzy set; L-fuzzy set; Uncertainty; p-conjugate; T operation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s12543-011-0064-y

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